Operator docstrings displayed on buttons, not in search mode
Spacebar search uses bpy.types.Menu type class to display content in contrast of bpy.types.Panel for buttons etc.

Drawing methods in both of them will be the same, like:

def draw(self, context):
    self.layout.operator(...)


Menu will have the items with displayed shortcuts aside with no box popup (this is probably because a menu can have a sub-menu as a popup so to not confuse).

Panel formatting has more options and does show the pop-up doc-string.

This is by some design decision and cannot be changed with current exposed api.